Common Description:
Light Chemicals is an industrial paint supplier with presence in three locations: Mumbai, Hyderabad and Bengaluru. The sunburst chart below shows the distribution of the number of employees of different departments of Light Chemicals. There are four departments: Finance, IT, HR and Sales. The employees are deployed in four ranks: junior, mid, senior and executive. The chart shows four levels: location, department, rank and gender(M: male, F: female). At every level, the number of employees at any location/department/rank/gender are proportional to the corresponding area of the region represented in the chart.
Due to some issues with the software, the data on junior female employees have gone missing. Notice that there are junior female employees in Mumbai HR, Sales and IT departments, Hyderabad HR department, and Bengaluru IT and Finance departments: the corresponding missing numbers are marked u, v, w, x, y and z in the diagram, respectively.
It is also known that:
a) Light Chemicals has a total of 210 junior employees.
b) Light Chemicals has a total of 146 employees in the IT department.
c) Light Chemicals has a total of 77 employees in the Hyderabad office.
d) In the Mumbai office, the number of junior female employees is 55.
Based on the given information and the sunburst chart, which of the following has the HIGHEST number of employees?
A
Step-by-Step Solution
Key idea: This is a hierarchical data aggregation question, recognizable because it asks for the maximum value across different levels of a sunburst chart.
Step 1: Use the given totals to set up equations. Total junior employees = 210. Summing all junior segments gives: 25 + w + 30 + v + u + 15 + 18 + z + 16 + y + x + 10 = 210, which simplifies to u + v + w + x + y + z = 96.
Step 2: Total IT employees = 146. Summing IT segments gives: 22 + 15 + 25 + w + 14 + 8 + 16 + y + 12 + 10 = 146, which simplifies to w + y = 24.
Step 3: Total Hyderabad employees = 77. Summing Hyderabad segments gives: 13 + 11 + 9 + 7 + x + 10 + 9 + 6 = 77, which gives x = 12.
Step 4: Mumbai junior female employees = 55. This means w + v + u = 55.
Step 5: Substitute x = 12 into the first equation: u + v + w + y + z = 84. Since w + y = 24, we can deduce relationships. More directly, from u + v + w = 55 and u + v + w + x + y + z = 96, we get x + y + z = 41. With x = 12, we get y + z = 29.
Step 6: Evaluate the options.
- IT department total is explicitly given as 146.
- Bengaluru office total = 22 + 20 + 18 + z + 16 + y + 12 + 10 + 8 + 6 = 112 + y + z. Since y + z = 29, Bengaluru total = 112 + 29 = 141. (Wait, let's re-add: 22+20+18+16+12+10+8+6 = 112. 112 + 29 = 141).
- Mumbai Sales department = 30 + v + 12 + 10 = 52 + v. Since w + v + u = 55 and w, u > 0, v < 55. Thus, Mumbai Sales < 107.
- Mid-level, all offices = 22 + 15 + 18 + 12 + 20 + 22 + 13 + 11 = 133.
Step 7: Compare the totals. IT department (146) is strictly greater than Bengaluru (141), Mumbai Sales (<107), and Mid-level (133).
Answer: IT department, all offices together.